st: Re: Econometrically sound to use Mills ratio after mprobit?

I haven't come across such paper, however there have been several papers
dealing with selectivity-adjustment using the conditional probabilities of a
multinomial logit.

Check: -svyselmlog- (downloadable from SSC) and the references there.

The main point of debate is how to parameterize the conditional
probabilities: (1) make a normal transformation, (2) include the cond.
probabilities of the those categories not chosen, (3) semi-parametric
methods.

If you come across such paper, please let me know. I would be interested in
exploring the possibility of writing such a code.

I am estimating a multinomial probit for a selection equation with 3
choices and I am interested in using the inverse mills ratio generated
from the MNP in a second step equation. I know how to implement this
procedure, however, I have not been able to find any literature that
proves that the Heckman two-step estimation procedure can appropriately
and directly extend from a probit selection equation to a multinomial
probit selection equation. Does anyone know of any papers that address
this issue?